Properties

Label 2496.1.l
Level $2496$
Weight $1$
Character orbit 2496.l
Rep. character $\chi_{2496}(1793,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $448$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2496.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(448\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2496, [\chi])\).

Total New Old
Modular forms 48 10 38
Cusp forms 24 6 18
Eisenstein series 24 4 20

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q - 2 q^{9} + O(q^{10}) \) \( 6 q - 2 q^{9} + 6 q^{13} + 2 q^{25} - 2 q^{49} + 4 q^{61} - 8 q^{69} + 6 q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2496, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2496.1.l.a 2496.l 39.d $1$ $1.246$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}+q^{13}-q^{25}-q^{27}-q^{39}+\cdots\)
2496.1.l.b 2496.l 39.d $1$ $1.246$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}+q^{13}-q^{25}+q^{27}+q^{39}+\cdots\)
2496.1.l.c 2496.l 39.d $4$ $1.246$ \(\Q(\zeta_{8})\) $D_{4}$ None \(\Q(\sqrt{39}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2496, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2496, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)